Local coupling Noise induced nucleations

Local coupling among excitable elements is realized through diffusive coupling, which introduces spatial degree of freedom in the system. Here we consider the case of an one-dimensional Oregonator system in its three-component version. Thus its local dynamic introduced in subsection 1.2.3, see Eqs, 1.2 has to be supplemented by diffusion terms. As in the experiment with the BZ reaction the catalyst is immobilized in thin gel layer, there is no diffusion in the v variable. This gives 

We integrate numerically Eqs. 1.37 in a one dimensional spatial domain of size L with periodic boundary conditions. 

Here r] x, t) is a spatio-temporally correlated noise process with zero mean, characterized by noise intensity cj, correlation time r and correlation length A. For more detail on the numerical details see [5]. 

Suppose the medium is prepared in the homogeneous steady state. Eventually, fluctuations of the light intensity induce spontaneous nucleation 

To characterize the coherence of noise-induced patterns in the distributed excitable medium we calculate the relative fluctuations of the spatial average C/i(t) of the activator field u x,t) 

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